Ebook: Mathematics and Computer Science in Medical Imaging

Medical imaging is an important and rapidly expanding area in medical science. Many of the methods employed are essentially digital, for example computerized tomography, and the subject has become increasingly influenced by develop­ ments in both mathematics and computer science. The mathematical problems have been the concern of a relatively small group of scientists, consisting mainly of applied mathematicians and theoretical physicists. Their efforts have led to workable algorithms for most imaging modalities. However, neither the fundamentals, nor the limitations and disadvantages of these algorithms are known to a sufficient degree to the physicists, engineers and physicians trying to implement these methods. It seems both timely and important to try to bridge this gap. This book summarizes the proceedings of a NATO Advanced Study Institute, on these topics, that was held in the mountains of Tuscany for two weeks in the late summer of 1986. At another (quite different) earlier meeting on medical imaging, the authors noted that each of the speakers had given, there, a long introduction in their general area, stated that they did not have time to discuss the details of the new work, but proceeded to show lots of clinical results, while excluding any mathematics associated with the area.

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Content:
Front Matter....Pages I-VIII
Front Matter....Pages 1-1
Introduction to Integral Transforms....Pages 3-42
Introduction to Discrete Reconstruction Methods in Medical Imaging....Pages 43-65
Image Structure....Pages 67-104
Fundamentals of the Radon Transform....Pages 105-125
Regularization Techniques in Medical Imaging....Pages 127-141
Statistical Methods in Pattern Recognition....Pages 143-166
Image Data Compression Techniques: A Survey....Pages 167-195
From 2D to 3D Representation....Pages 197-220
VLSI-Intensive Graphics Systems....Pages 221-240
Knowledge Based Interpretation of Medical Images....Pages 241-266
Front Matter....Pages 267-267
The Attenuated Radon Transform....Pages 271-277
Inverse Imaging with Strong Multiple Scattering....Pages 279-289
Possible Criteria for Choosing the Number of Iterations in Some Iterative Reconstruction Methods....Pages 293-303
Initial Performance of Block-Iterative Reconstruction Algorithms....Pages 305-317
Maximum Likelihood Reconstruction in PET and TOFPET....Pages 319-329
Maximum Likelihood Reconstruction for SPECT Using Monte Carlo Simulation....Pages 331-338
X-Ray Coded Source Tomosynthesis....Pages 339-349
Some Mathematical Aspects of Electrical Impedance Tomography....Pages 351-362
Hierarchical Figure-Based Shape Description for Medical Imaging....Pages 365-387
GIHS: A Generalized Color Model and Its Use for the Representation of Multiparameter Medical Images....Pages 389-399
Front Matter....Pages 267-267
The Evaluation of Image Processing Algorithms for Use in Medical Imaging....Pages 401-414
Focal Lesions in Medical Images: A Detection Problem....Pages 415-437
Time-Domain Phase: A New Tool in Medical Ultrasound Imaging....Pages 441-454
Performance of Echographic Equipment and Potentials for Tissue Characterization....Pages 455-468
Development of a Model to Predict the Potential Accuracy of Vessel Blood Flow Measurements from Dynamic Angiographic Recordings....Pages 469-478
The Quantitative Imaging Potential of the HIDAC Positron Camera....Pages 479-490
The Use of Cluster Analysis and Constrained Optimisation Techniques in Factor Analysis of Dynamic Structures....Pages 491-503
Detection of Elliptical Contours....Pages 505-515
Optimal Non-Linear Filters for Images with Non-Gaussian Differential Distributions....Pages 517-525
Back Matter....Pages 527-548

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Content:
Front Matter....Pages I-VIII
Front Matter....Pages 1-1
Introduction to Integral Transforms....Pages 3-42
Introduction to Discrete Reconstruction Methods in Medical Imaging....Pages 43-65
Image Structure....Pages 67-104
Fundamentals of the Radon Transform....Pages 105-125
Regularization Techniques in Medical Imaging....Pages 127-141
Statistical Methods in Pattern Recognition....Pages 143-166
Image Data Compression Techniques: A Survey....Pages 167-195
From 2D to 3D Representation....Pages 197-220
VLSI-Intensive Graphics Systems....Pages 221-240
Knowledge Based Interpretation of Medical Images....Pages 241-266
Front Matter....Pages 267-267
The Attenuated Radon Transform....Pages 271-277
Inverse Imaging with Strong Multiple Scattering....Pages 279-289
Possible Criteria for Choosing the Number of Iterations in Some Iterative Reconstruction Methods....Pages 293-303
Initial Performance of Block-Iterative Reconstruction Algorithms....Pages 305-317
Maximum Likelihood Reconstruction in PET and TOFPET....Pages 319-329
Maximum Likelihood Reconstruction for SPECT Using Monte Carlo Simulation....Pages 331-338
X-Ray Coded Source Tomosynthesis....Pages 339-349
Some Mathematical Aspects of Electrical Impedance Tomography....Pages 351-362
Hierarchical Figure-Based Shape Description for Medical Imaging....Pages 365-387
GIHS: A Generalized Color Model and Its Use for the Representation of Multiparameter Medical Images....Pages 389-399
Front Matter....Pages 267-267
The Evaluation of Image Processing Algorithms for Use in Medical Imaging....Pages 401-414
Focal Lesions in Medical Images: A Detection Problem....Pages 415-437
Time-Domain Phase: A New Tool in Medical Ultrasound Imaging....Pages 441-454
Performance of Echographic Equipment and Potentials for Tissue Characterization....Pages 455-468
Development of a Model to Predict the Potential Accuracy of Vessel Blood Flow Measurements from Dynamic Angiographic Recordings....Pages 469-478
The Quantitative Imaging Potential of the HIDAC Positron Camera....Pages 479-490
The Use of Cluster Analysis and Constrained Optimisation Techniques in Factor Analysis of Dynamic Structures....Pages 491-503
Detection of Elliptical Contours....Pages 505-515
Optimal Non-Linear Filters for Images with Non-Gaussian Differential Distributions....Pages 517-525
Back Matter....Pages 527-548
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